Question

1/cos0.cos1 + 1/cos1.cos2 +1/cos2.cos3 +.....+1/cos88.cos89 =?

Answer 1

Answer:

1/cos0.cos1 + 1/cos1.cos2 +1/cos2.cos3 +.....+1/cos88.cos89 = Cos1/(1 - Cos²1)

Step-by-step explanation:

1/cos0.cos1 + 1/cos1.cos2 +1/cos2.cos3 +.....+1/cos88.cos89 =?

multiply & Divide by Sin1

= (1/Sin1) {Sin1/cos0.cos1 + Sin1/cos1.cos2 +Sin1/cos2.cos3 +.....+Sin1/cos88.cos89)

=(1/Sin1) {Sin(1-0)/cos0.cos1 + Sin(2-1)/cos1.cos2 +Sin(3-2)/cos2.cos3 +.....+Sin(89-88)/cos88.cos89)

Sin(A-B)/CosACosB = (SinACosB - CosASinB)/CosACosB = TanA - TanB

= (1/Sin1) {(Tan1 - Tan0) + (Tan2 - Tan1) + (Tan3 - Tan2) +.............. + (Tan89 - Tan88)

=(1/Sin1)( (Tan1 + Tan2 + Tan3 +.............+ Tan89)-(Tan0 + Tan1 + Tan2 +......... + Tan88))

=(1/Sin1) (Tan89 + (Tan1 + Tan2 +......... + Tan88) - (Tan1 + Tan2 +......... + Tan88) - Tan0)

=(1/Sin1) ( Tan89 - Tan0)

Tan 0 = 0

= (1/Sin1)(Tan89)

Tan 89 = Cot1

= (1/Sin1)(Cot1)

= (1/Sin1)(Cos1/Sin1)

= Cos1/Sin²1

= Cos1/(1 - Cos²1)